Bob, I always find this sort of thing somewhat confusing and do in general have as many questions as answers in matters of grammar. “He flew to London by aeroplane.” BY, as Erik says, is a preposition. But the question I ask is how is it functioning as a preposition, and looking up the definition of preposition isn’t that helpful in explaining it. Fowler defines a preposition as “a word governing (and usually preceding) a noun or pronoun and expressing a relation to another word or element.” This is vague enough not to really tell you how to tell if something is being used as a preposition and what function a particular preposition is playing.

One thing I can say for my elementary school education in Brooklyn in the 1940s was that they really drummed certain grammar things into my head (right or wrong, but I think mostly right) – although you might never know it by listening to some of my compatriots speaking Brooklynese. And one of these things was the perhaps simplistic view that certain parts of speech answer certain questions. A preposition answered the questions ‘where,’ ‘when,’ ‘how,’ and ‘why.’ ‘The ‘where’ involved questions of place and direction (e.g. on, up, down, between, under, at, to, toward). The ‘when’ answered questions of time (e.g. before, during, after, until, while, since, by, for, on, at). The ‘how’ was a little trickier and answered, among other things, questions of ‘by what means’ (e.g. flew ‘by’ plane, runs ‘on’ coal, cut it ‘with’ a knife, he died ‘of’ old age, she suffered ‘from’ arthritis, he walked ‘instead of’ driving). And there are, of course, prepositions that answer other aspects of how, such as he walked ‘by’ himself. The ‘why’ answered questions of cause or reason (e.g. because of, for,). And I’m sure there are other prepositions that don’t fit neatly into the above categories, but I did find this ‘answering the questions’ method generally useful.

As an aside, one question that I have is, when people says they ‘flew by airplane’ they are saying they ‘flew by means of an airplane,’ and that tells how they flew. Does that then make the prepositional phrase ‘by airplane’ an adverbial prepositional phrase – if there is such a thing. And similarly when one says he went ‘by himself’ is that also an adverbial phrase telling how he went. This is just a matter of terminology, but I’m curious about the ‘official’ nomenclature.
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And lest we forget there is that famous astronomical unit of measure the BY-PARSEC defined as the unit of distance equal to that required to cause a heliocentric parallax of two seconds of an arc, equivalent to 412,530 times the distance from the earth to the sun, or 6.52 light-years!!